Problem: Solve for $p$. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. $-31p+79 > -59p + 81$
Solution: $\begin{aligned}-31p+79 & > -59p + 81 \\\\ -31p&> -59p+2 &(\text{Subtract } 79 \text{ from both sides}) \\\\ 28p &> 2 &(\text{Add } 59p \text{ to both sides})\\\\ p&>\dfrac{1}{14}&(\text{Divide both sides by }28 \text{ and simplify}) \end{aligned}$ In conclusion, the answer is $p > \dfrac{1}{14}$.